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Pure Maths Junior Seminar 26-27
For the first semester, the seminar takes place every other Monday at 4 pm in tutorial room 3B of the School of Mathematics and Statistics of the University of St Andrews.
Autumn Semester
Week | Date | Speaker(s) | Institute | Title | Abstract |
|---|---|---|---|---|---|
Week 3 | 28/09/2026 | Henry Phillips | University of St Andrews | An introduction to modern symplectic geometry | After beginning with some historical motivation and introductory definitions, we will introduce some J-holomorphic curve theory and prove Gromov's non-squeezing theorem, which shows some surprising rigidity of symplectic geometry. The talk will be accessible and (hopefully) interesting to all. |
Week 5 | 12/10/2026 | Callum Barber | University of St Andrews | Congruences vs Diagonal Subsemigroups | A congruence is one of the most fundamental objects used in universal algebra; we use them to quotient algebraic structures. A much less studied object is that of a diagonal subalgebra. The bulk of my PhD has been studying the interplay between these two objects in the specific case when the algebra is a semigroup. I will talk through two ways to do this. The first is through what is called a DSC semigroup, which is a semigroup where every diagonal subsemigroup is a congruence. The second is the DSC coefficient, which is the ratio of congruences to diagonal subsemigroups on a finite semigroup. I shall give some (hopefully) interesting results on both of these. |
Week 7 | 26/10/2026 | Manuel Leal | Alfréd Rényi Institute | Noether-Lefschetz theory and determinantal surfaces | This talk is about algebraic surfaces in the projective space P3. The starting point is the Noether-Lefschetz theorem, which asserts the following: if a surface X in P3 is very general, then every algebraic curve contained in X is the intersection of X with another surface.
The set of surfaces which are not "very general", in the sense of the Noether-Lefschetz theorem, is very complicated. It is a countable union of families, known as Noether-Lefschetz components, which are the object of study of the so-called Noether-Lefschetz theory.
The first part of the talk will be an overview of the basic definitions, classic results, and open problems in Noether-Lefschetz theory. Afterwards, I will introduce a special class of surfaces: determinantal surfaces. I will explain the relation between determinantal surfaces and Noether-Lefschetz components, and what this tells us in the context of Noether-Lefschetz theory. This talk is based on joint work with César Lozano Huerta and Montserrat Vite. |
Week 9 | 09/11/2026 | Ella Yates | University of Glasgow | TBC | |
Week 11 | 23/11/2026 | Yuyang Liu / Peizhi Liu | University of St Andrews | TBC |
Organisers: Violeta Lopez Lopez, Joe Edwards, Saeed Shaabanian.
This is the second consecutive year that this seminar series has been running. You can view the previous year's seminar in the following link.
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